A Note on Dominating Pair Degree Condition for Hamiltonian Cycles in Balanced Bipartite Digraphs

Let D be a strong balanced bipartite digraph on 2 a vertices. For x , y , z ∈ V ( D ) , if x → z and y → z , then we call the pair { x , y } dominating; if z → x and z → y , then we call the pair { x , y } dominated. In 2017, Adamus [Graphs and Combinatorics, 33(2017) 43–51] proved that if d ( x ) +...

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Vydané v:Graphs and combinatorics Ročník 38; číslo 1
Hlavný autor: Wang, Ruixia
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Tokyo Springer Japan 01.02.2022
Springer Nature B.V
Predmet:
Apexes
Combinatorial analysis
Combinatorics
Engineering Design
Graph theory
Lower bounds
Mathematics
Mathematics and Statistics
Original Paper
05C20
Balanced bipartite digraph
Hamiltonian cycle
Degree sum condition
Dominating pair
ISSN:0911-0119, 1435-5914
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Popis
Shrnutí:Let D be a strong balanced bipartite digraph on 2 a vertices. For x , y , z ∈ V ( D ) , if x → z and y → z , then we call the pair { x , y } dominating; if z → x and z → y , then we call the pair { x , y } dominated. In 2017, Adamus [Graphs and Combinatorics, 33(2017) 43–51] proved that if d ( x ) + d ( y ) ≥ 3 a whenever { x , y } is a dominating or dominated pair, then D is Hamiltonian. In 2021, Adamus [Discrete Mathematics, 344(3) (2021) 112240] proved that if only every dominating pair of vertices { x , y } in D satisfies d ( x ) + d ( y ) ≥ 3 a + 1 , then D is Hamiltonian. In this paper, we show that the same conclusion is reached if we replace 3 a + 1 with 3 a in the above condition. The lower bound for 3 a is sharp.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-021-02404-8